Related papers: Pixel Arrays: A fast and elementary method for sol…
One of the main limitations for the resolution of optical instruments is the size of the sensor's pixels. In this paper we introduce a new sub pixel resolution algorithm to enhance the resolution of images. This method is based on the…
The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
Newton-type solvers have been extensively employed for solving a variety of nonlinear system of algebraic equations. However, for some complex nonlinear system of algebraic equations, efficiently solving these systems remains a challenging…
Motivated by the mathematics literature on the algebraic properties of so-called polynomial vector flows, we propose a technique for approximating nonlinear differential equations by linear differential equations. Although the idea of…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
The problem of rectangle tiling binary arrays is defined as follows. Given an $n \times n$ array $A$ of zeros and ones and a natural number $p$, our task is to partition $A$ into at most $p$ rectangular tiles, so that the maximal weight of…
This paper presents a fast and robust method for fixed pattern noise nonuniformity correction of infrared focal plane arrays. The proposed method requires neither shutter nor elaborate calibrations and therefore enables a real time…
Pixel detectors typically display pixel-to-pixel gain variation of a few percent which result in reduced spectroscopic performance. We have developed a calibration method which relies on cross-correlating histograms of many pixel pairs and…
In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that we employ a particular embedding (Carleman linearization) to…
Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on…
We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…